3  The simulation model

The simulation model is an open economy, overlapping generations model. The essential features of the model are described here and the algebraic detail is given in the Appendix.

Households plan their consumption and labour supply over their entire lifetime, given known values of future income, the tax rate and the interest rate. (The plans of children are effectively made by their parents.) Each generation is characterised by one person household who dies at age 85 with certainty. A period of time is one year duration and a new generation of households is born each period, implying that there are h=85 overlapping generations of households alive at any time. The households supply labour between the age of 15 and 70; hence the retirement decision is exogenous and there are 66 generations of workers.

Households derive utility from consuming a composite index of private goods, leisure and public goods, the latter being exogenous and separable from both private consumption and leisure in generating utility, following the approach in Foertsch (2004). Households plan consumption and leisure over their lifecycle by maximising an intertemporal utility function.[6]

Households have full knowledge of future income, interest rates and tax rates until the policy shock arrives. The policy shock is the unexpected decision by government to adopt a new fiscal regime (tax smoothing in this case) in response to the fiscal pressures from ageing. Until that time households assume that the government will adopt an average tax rate that balances its budget in each period, implying a ‘pay-as-you-go' approach to the fiscal costs of ageing and a constant net debt to GDP ratio at its 2015 level. The new fiscal regime is a decision to adopt a constant tax rate from 2015. When this occurs, households re-optimise over the remainder of their lifetimes based on the implied future path of the tax rate; their past decisions are unaffected. For example an individual aged 60 at the time of the shock re-optimises for the remaining 25 years of life. An individual at age 20 re-optimises over the remaining 65 years of life.

The path of the tax rate affects households' optimal plans in two ways. The first is the intratemporal decision to consume goods and services relative to leisure (time spent not working). This is affected by the relative price of leisure which is the after-tax real wage rate. A higher tax rate reduces the price of leisure and therefore discourages labour participation. This is the substitution effect and is the source of the deadweight loss from taxing labour. On the other hand a higher tax rate also reduces disposable income which tends to reduce both consumption and leisure (therefore increasing labour participation). This is the income effect which does not give rise to a deadweight loss because it represents a transfer of income among households, given that taxation ultimately finances spending. The second way in which the path of the tax rate affects household plans is an intertemporal effect. Household saving decisions reflect their allocation of consumption between the present and the future. They balance the cost of saving (their rate of time preference) against the return to saving (the after-tax interest rate). A higher tax rate[7] lowers the return to saving and therefore raises present consumption relative to future consumption. The wedge driven between the return to saving and the cost of saving is the source of the deadweight loss from taxation of capital.

The lifecycle path of disposable labour income and consumption is illustrated in Figure 3 for the generation born in 2015.

Figure 3 - Household labour income (after tax) and consumption. Balance Budget scenario. Medium fertility

Households supply labour to a representative firm that combines the aggregate labour with capital according to Cobb-Douglas technology and produces a single good. The firm determines its capital-labour ratio by equating the marginal cost of capital with the cost of capital, which is assumed to be constant. The firm demands labour up to the point where the marginal product of labour is equal to the real wage. The real wage adjusts instantaneously to equate labour demand to labour supply.

Government spending is an exogenously given share of GDP, but since GDP is endogenous through endogenous labour supply the level of government spending is also endogenous.

All government spending other than transfer payments is assumed for simplicity to be government consumption spending. Hence

where G^C_j is government consumption spending and G^T_j is transfer payments. The government faces the following dynamic budget constraint:

where D_j^gov is government debt (net) and T_j is total taxes. The balanced budgets simulation implies debt sustainability since the debt to GDP ratio is constant throughout the projection period. For other simulations a sustainable debt path is defined as one that returns to the initial debt to GDP ratio at the end of the projection period.